JetBlue Airways resumed full operations at Logan International Airport and three New York-area airports on Tuesday after a 17-hour shutdown forced the cancellation of more than 500 departures from the four facilities.

The highly unusual reduction in service followed a spell of bad weather and airport closures over the weekend, complicated by new federal regulations that require longer rest periods for pilots between flights. Those rules helped turn delays into more cancellations after pilots maxed out their hours.

JetBlue experienced more problems than most carriers, in part because most of its operations go through Boston and New York, which were hit hard by snow and ice.

John F. Kennedy International Airport in New York closed several times over the weekend, causing a ripple effect of delays, diversions, and cancellations throughout the system.

Over six days starting Thursday, JetBlue was responsible for 1,800 of the 20,000 cancellations industrywide, said Rob Maruster, the airline’s chief operating officer.

JetBlue was fully operational by Tuesday afternoon, but some stranded passengers will be unable to get flights out until next week. The delays in getting people home are partly due to flights that were 90 percent full during the holidays, leaving few open seats for bumped passengers.

WENDY MAEDA/GLOBE STAFF

The frustration was evident as passengers waited at Logan Airport on Tuesday to rebook flights. More than 1,300 arrivals and departures have been canceled since Jan. 2.

“When you have this level of an event over this many days and particularly when customers may be canceled one, two, and three times, often they just give up and find their own way,” Maruster said.

David and Ingrid Bates did just that when they found out Monday that their family’s JetBlue flight out of West Palm Beach, Fla., had been canceled for a third time. When they couldn’t find seats on any airline back to any airport within 500 miles of Boston, they packed their three children and Ingrid’s mother into a rented minivan and hit the road.

They spent Monday night in Savannah, Ga., and hoped to make it home to Brookline by Wednesday — almost a week later than they were supposed to return.

“It’s kind of like a roller coaster,” Ingrid said. “Yesterday, I didn’t know whether to laugh or cry.”

She did a bit of both, she admitted.

Over the course of six days, about 150,000 JetBlue customers had at least one flight canceled. The airline is compensating displaced passengers with frequent flier points and travel vouchers ranging from $50 to $200 in value, depending on the number of flights canceled.

But $100 isn’t doing much to assuage Charles Nessralla’s outrage.

The University of Massachusetts Medical School student and his sisters were supposed to leave the Dominican Republic on Monday, but they can’t get out until Saturday.

The siblings estimate they have paid more than $3,000 for lodging and phone charges to extend their stay, and the $100 travel voucher Nessralla is receiving “is nothing more than an insult,” he said.

“I will absolutely never fly JetBlue again,” he wrote in an e-mail.

JetBlue is more proactive about canceling flights before bad weather hits than in the past, Maruster said, which keeps passengers from going to the airport only to have their flight canceled. But it also means the airline sometimes takes what turn out to be unnecessary measures, as was the case with the “flash freezing” forecast for Monday night, which was not as bad as predicted.

JetBlue realized early on that the new pilot rest rules could wreak havoc on airline schedules if they were implemented in early January, as planned, because of the convergence of holiday travel and possible winter storms. So in September, the carrier asked the Federal Aviation Administration for flexibility to implement the regulations on a different date. The FAA denied the request, the airline said.

The FAA did not reply to a request for comment.

JetBlue supports the new rules, Maruster said, but added that when bad weather causes delays, the more restrictive requirements on how long a pilot can work will inevitably lead to more cancellations.

The Massachusetts Port Authority, which runs Logan, reported that terminals were returning to normal Tuesday after nearly a week of delays and cancellations. In all, more than 1,300 arrivals and departures at Logan have been canceled since Jan. 2, about a quarter of all flights at the airport, according to FlightView, a flight-tracking site based in Newton. JetBlue accounted for nearly 40 percent of those cancellations.